Nathan, a free agent, and the Tigers reached agreement Tuesday on a two-year contract, according to the highly reliable Bob Nightengale of USA TODAY Sports and Jon Heyman of CBSSports.com. Fox Sports reported the deal is in the $20 million range. That $10 million average doesn’t break any barriers; it is worth $4 million less per year than closer Rafael Soriano got on his two-year deal with Washington last off-season.

As of Tuesday night, the Tigers hadn’t announced the signing. Based on precedent, they probably wouldn’t say anything until Nathan passed a physical.

Nathan, who saved 43 games for Texas this season, fills the Tigers’ gaping vacancy for the single most crucial role on virtually any team with championship aspirations: ninth-inning closer.

Joaquin Benoit, who superbly stepped into that role for the Tigers in the second half of the regular season this year, is a free agent. This year marked Benoit’s first extensive work in closing, while Nathan has made a successful career of it. That could explain why the Tigers have chosen Nathan instead of Benoit as their closer.

In the crowded market of free-agent closers, Nathan has the best credentials. In each of his eight full non-injury seasons as a closer, he has recorded between 36 and 47 saves. (He has bounced back superbly from the elbow surgery that cost him all of 2010.)

Nathan will be 39 throughout next season, but several closers have flourished at that age and older. There have been 11 times in big-league history that a pitcher recorded at least 30 saves in the season he was 39 or older. Mariano Rivera leads with four such seasons, and Trevor Hoffman had three. (For purposes of this statistic, a player’s age is his age on June 30, the approximate mid-point of the season).

Just as they know from their experience how dominant Nathan can be, the Tigers also know that a closer can be effective at 39. Todd Jones was that age when he saved 38 games for the Tigers in 2007.

Nathan retains a key trait of durability for a closer. He can pitch effectively three days in a row. There were eight times this season where he pitched after having pitched the two previous days. Although he looked rocky in some of those eight outings, he gave up only one run combined in them.

Nathan twice pitched four days in a row — including the final four days of the season, when Texas had to win daily in order to maintain its playoff chances. In those four season-ending games, he pitched a total of four innings and allowed one hit, one walk and no runs. He had plenty left in the tank, and how he gets the whole off season as a fill-up.

Nathan has acknowledged that his average velocity is down a few miles per hour from his peak. But his slider was better than ever this year, and he used his curve effectively.

The result was that, at 38, he had one of his best seasons. He allowed less than one runner per inning and thereby turned in the second-lowest WHIP of his career. That’s the statistic that reflects how stingy a pitcher is about allowing runners — it represents walks and hits allowed combined, divided by innings pitched.

Nathan still throws above 90 m.p.h., and when he really needs to, he can still reach his old peak of about 96 m.p.h.

Nathan blew three saves this year. On rare occasions such as those when he doesn’t get the job done, he is at his locker immediately after the game to take reporters’ questions. He doesn’t leave it to his teammates to explain his downfall. This trait, known as being “a stand-up guy,” is reminiscent of Jones and the respect he commanded as the Tigers closer.

The Rangers didn’t want to offer Nathan more than a one-year deal. He will like this two-year deal with the Tigers because it allows him to attain one of his goals: pitch at age 40, which he would do in the second year of the contract.

Unlike some closers, Nathan pitches to the score. If he has a multi-run lead, he is highly conscious of not walking the leadoff hitter in the ninth to bring up the potential tying run. He will reduce his velocity to make sure he throws strikes. He will make that leadoff man hit his way on base.

Nathan came up through the Giants system primarily as a starter. The Twins made him a closer in as soon as they obtained him in a larcenous trade from San Francisco, and for his first four seasons in Minnesota, he was a teammate of Torii Hunter.

Now Nathan — who has never played on a team that won a post-season series — has joined Hunter on the Tigers at the culmination of his career as each tries to reach the World Series for the first time.

Contact John Lowe: jlowe@freepress.com. Follow him on Twitter @freeptigers.